Problema Solution
A cubical vessel contains 2048 cubic meters of water when half-full. Find the total surface area of the vessel and the length of its diagonal.
Answer provided by our tutors
let
a = the length of the side of the cubic vessel, a>o
d = the length of the diagonal, d>0
V/2 = 2048 m^3, where V is the volume of the cube
A = the surface area of the cube
the volume of the cube is V = a^2 thus
(1/2)a^3 = 2048
by solving we find:
a = 16 m
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the total surface of the cube is: A = 6 a^2
A = 6*(16^2)
A = 1,536 m^2
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the total surface area of the vessel is 1,536 m^2.
using the Pythagorean theorem we find the diagonal:
d^2 = a^2 + a^2 + a ^2
d^2 = 3a^2
d^2 = 3*16^2
we find:
d = 27.71 m
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the length of the diagonal is 27.71 m.